Hi,
I've been struggling with this problem for a while now. A 52 card deck is dealt out randomly to 4 players who get 13 cards each. What is the probability that one of the players receives at least two aces? I was thinking something along the lines of 52!/(13!*13!*13!*13!) but I'm not sure I'm heading in the right direction. Can someone please share some insight to this? Thanks.
Lay out the four aces and write a number from 1 to 4 above each indicating the player who receives that ace. This can be done in 4^4 ways, each of which are equally likely. Each player receives exactly one ace when the numbers are a permutation of 1-2-3-4, which can be done in 4! ways.